geometry

Outside of circle Γ, point A is chosen. Tangents AB and AC to Γ are drawn, with B,C on the circumference of Γ. On the extension of AB, D is a point such that B is between A and D, and ∠ADC=25∘. The circumcircle of ADC intersects Γ again at E (different from point C ). F is the foot of the perpendicular from B to DC. What is the measure (in degrees) of ∠DEF?

Outside of circle Γ, point A is chosen. Tangents AB and AC to Γ are drawn, with B,C on the circumference of Γ. On the extension of AB, D is a point such that B is between A and D, and ∠ADC=25∘. The circumcircle …

Let AB be the diameter of circle Γ1. In the interior of Γ1, there are circles Γ2 and Γ3 that are tangent to Γ1 at A and B, respectively. Γ2 and Γ3 are also externally tangent at C. This exterior tangent …

Circle Γ with center O has diameter AB=192. C is a point outside of Γ, such that D is the foot of the perpendicular from C to AB and D lies on the line segment OB. From C, a tangent to Γ is drawn, touching Γ at …

Given circle Γ and a point P outside of Γ, 2 lines l1 and l2 are drawn such that both pass through P. l1 intersects Γ at A and B, and l2 intersects Γ at C and D, with C between D and P. If PA=44,PB=294 and PC=56, …